Can someone please help me with this problem?

Mathematics

2 answers:

omeli [17]3 years ago

5 0

I think is the one on the top left but not really sure, and wish you luck with that lesson.

Rom4ik [11]3 years ago

4 0

The answer is d
square 4. multiply the result by 7, and then subtract 5.

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Does the set {t, t Int} form a fundamental set of solutions for t^2y" -- ty' +y = 0?

Ivanshal [37]

Answer:

yes

Step-by-step explanation:

We are given that a Cauchy Euler's equation

$t^2y''-ty'+y=0$ where t is not equal to zero

We are given that two solutions of given Cauchy Euler's equation are t,t ln t

We have to find the solutions are independent or dependent.

To find the solutions are independent or dependent we use wronskain

$w(x)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}$

If wrosnkian is not equal to zero then solutions are dependent and if wronskian is zero then the set of solution is independent.

Let $y_1=t,y_2=t ln t$

$y'_1=1,y'_2=lnt+1$

$w(x)=\begin{vmatrix}t&t lnt\\1&lnt+1\end{vmatrix}$

$w(x)=t(lnt+1)-tlnt=tlnt+t-tlnt=t$ where t is not equal to zero.

Hence,the wronskian is not equal to zero .Therefore, the set of solutions is independent.

Hence, the set {t , tln t} form a fundamental set of solutions for given equation.

6 0

3 years ago

Refer to the photo :D

OlgaM077 [116]

well, we know the ceiling is 6+2/3 high, and Eduardo has 4+1/2 yards only, how much more does he need, well, is simply their difference, let's firstly convert the mixed fractions to improper fractions and then subtract.

$\stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} ~\hfill \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{20}{3}-\cfrac{9}{2}\implies \stackrel{using ~~\stackrel{LCD}{6}}{\cfrac{(2\cdot 20)-(3\cdot 9)}{6}}\implies \cfrac{40-27}{6}\implies \cfrac{13}{6}\implies\blacktriangleright 2\frac{1}{6} \blacktriangleleft$